Solve the quadratic equation by completing the square

Question

Solve by completing the square.

2x²+4x-2=0

Answer 1

Answer 2

Given:

2x² + 4x - 2 = 0

Completing the square is an awesome tool for solving quadratics, but it has one strict rule we have to follow before we start: the number in front of our x² must be a 1.

Since we have a 2 in front of our x², we need to divide every term in the equation to get rid of it:

2x² + 4x - 2 = 0

x² + 2x -1 = 0

Now, we have to bring the constant term (-1) over to the other side by adding 1 to both sides:

x² + 2x = 1

Now comes the actual "completing the square". We need to find the perfect number to add to both sides so that the left side becomes a perfect square trinomial.

To find that number, we take the number in front of our x (which is 2), cut it in half, and square it:

Half of 2 = 1

1² = 1

So, the number we need is 1! Now, we add it to both sides of our equation:

x² + 2x + 1 = 1 + 1

x² + 2x + 1 = 2

The left side can now be factored and rewritten as the perfect square (x + 1)². You can check this by foiling out (x + 1)², and you'll get x² + 2x + 1.

Let's rewrite the equation with our perfect square:

(x + 1)² = 2

We can now solve for x by taking the square root of both sides:

(x + 1)² = 2

√((x + 1)²) = ±√2 (Don't forget the ± when taking a square root!)

Simplify it more:

x + 1 = ±√2

Now solve for x:

x = -1 ± √2

This gives two final answers:

x = -1 + √2 and x = -1 - √2

Answer 3

2x^2 +4x -2 = 0

divide by 2 to simplify

x^2 +2x -1 = 0

x^2 +2x +1 = 1 +1 = 2

(x+1)^2 = 2

x+1 = +/-sqr2

x = -1 +/-sqr2= about -1+/-1.414

x = about - 2.414 or 0.414

Answer 4

Solve the following equation by completing the square:

2x ² + 4x - 2 = 0

First divide every term in the equation by 2 to get rid of the x ² coefficient. This gives us:

X ² + 2X -1 = 0

Next add 1 to both sides of the equation to move the constant over to the right side of the equation:

X ² + 2X = 1

Next divide the coefficient of X by 2, square the result, and add that result to both sides of the equation:

X ² + 2X + 1 = 2

Next divide the coefficient of X by 2 and this value is used with X to factor the left side of the equation, which by the above steps was manipulated into being a perfect square:

(X + 1)² = 2

Now take the square root of both sides of the equation in an attempt to solve for X.

√ (X +1)² = ± √ 2

This becomes:

X + 1 = ± √ 2

Finally subtract 1 from each side of the equation to get the variable X alone on one side and the constant on the other side of the equation:

X = -1 ± √ 2

This solves the quadratic equation, 2X ² + 4X - 2 = 0 for the two values of X.

Answer 5

2x²+4x-2 = 0

Divide each term by 2, you get:

x²+2x-1=0

If I add 1 to the terms x²+2x, you get a perfect square (x+1)². So, I'll add 1 to both sides of the equation

x²+2x+1-1=1

The first 3 terms represent (x+1)²

(x+1)²-1 = 1

Add one to both sides

(x+1)² = 2

Take square root on both sides

(x+1) = ±√2

 

x = -1 ± √2

These are the roots for the polynomial given

Answer 6

Answer 7

How to solve a quadratic equation by completing the square